[Beowulf] improvements on floating point arithmetic
agshew at gmail.com
Fri Feb 6 10:04:40 PST 2015
I was a beta reader for "The End of Error: Unum Computing" by John
Gustafson, and I wanted to highly recommend it to everyone.
If you want to know more about the pitfalls of floating point arithmetic,
then you'll find it is a thorough and readable treatment. He also proposes
a new universal number format, unum, that extends the floating point format
with precision information and an "exact" bit.
He's created a Mathematica reference implementation, and has used it to
show how he can get better answers with less programmer work and moving
fewer bits. Among its benefits, unums also provide commutativity, which
means serial and parallel computations will give the same answer. Another
innovation that's particularly noteworthy is support for arithmetic using
opened and closed intervals. Unlike traditional interval arithmetic, his
bounds don't explode.
There's an old presentation at
http://sites.ieee.org/scv-cs/files/2013/03/Right-SizingPrecision1.pdf ... I
have a newer one, but didn't include it because I didn't want to spam
everyone with a 10MB attachment.
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